The Blues were linked with a move for the Paris Saint-Germain defender.
Silva has already confirmed he will leave the Ligue 1 champions after the Sunday’s Champions League final against Bayern Munich.
Frank Lampard was looking to add the 35-year-old’s experience to his shaky backline, but would now have to look at other alternatives.
But Silva is ready to take a huge pay cut to return to Serie A after eight years in France.
Thiago is believed to be earning a hefty £1.3million a month with the French giants and is thought to be targeting a two-year contract at his next club.